Pump issues

I have a well pump that is 2 years old. It repeatively goes of and on very quickly, when the pressure goes down to 20 lbs (where it is set) I have to hold it closed to make it fill back up to pressure. This is the 2nd new pressure switch I've installed in 2 days. I've check the lines and they are clear and there is no leaks in the bladder. Could the pump its self be bad? Or are there any switches I could adjust to make it work correctly? Right not when we use water I have to stand by the pump to make it pump back up to pressure.

As Hube suggested, the precharge in the tank should be set 2 psi less than pump cutin pressure, not 2 psi less than full pressure.
Since you said the pump comes on at 20 psi, the tank should be set at 18 psi. It needs to be completely drained when you set this pressure.
Ron